9. Special segments

9.01 Angle bisectors and perpendicular bisectors

9.02 Altitudes, medians, and bisectors of triangles

9.03 Inequalities in one triangle

Investigation: Proof of the triangle inequality

9.04 The triangle inequality

9.05 Extension: Geometric mean

9.06 Dividing a segment into a given ratio

United States of America UT

Math II

9.03 Inequalities in one triangle

Interactive practice questions

Consider the triangle in the figure:

A triangle with all its angles and sides labeled. The side measuring $13$ units is opposite of angle measuring $36^\circ$36°. The side measuring $17$ units is opposite of the angle measuring $47^\circ$47°. The side measuring $20$ units is opposite of the angle measuring $97^\circ$97°.

a

What is the sum of the interior angles in the triangle?

$\editable{}$°

b

Which side appears opposite the largest angle?

The longest side

A

The shortest side

B

The medium side

C

c

Which side appears opposite the smallest angle?

The shortest side

A

The medium side

B

The longest side

C

Easy

1min

Consider the triangle below.

Easy

< 1min

Consider the triangle below.

Easy

< 1min

Consider the triangle below.

Easy

< 1min

Outcomes

II.G.CO.10

Prove theorems about triangles. Theorems include: measures of interior angles of a triangle sum to 180°; base angles of isosceles triangles are congruent; the segment joining midpoints of two sides of a triangle is parallel to the third side and half the length; the medians of a triangle meet at a point.

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